Thank you all so much for the wonderful suggestions. I have pinking shears and iron-on stabilizer and can get some Fray Block at my local Joann's. I think it will be worthwhile watching the Fons and Porter video first, then doing some experimenting to see which will work best for me. It occurred to me in the middle of the night last night (as most of the most interesting thoughts do) that even if I got these silky pieces sewn into the blocks, and I was confident they wouldn't fray on the inside over time, I could get to the quilting part of the process only to find that quilting on this fabrics pulls threads or whatever, so I'll make a few practice blocks and quilt them before I get serious putting this thing together. Thank you again for all the great suggestions. If I remember, I'll come back and let you know how this experimenting worked out.